Cosmology

Participants: Dr MA Hendry, Dr K D'Mellow, Mr B Suprenant     
Collaborations: Marseille, Amherst, UHerts, Toulouse, Sissa, Sczeczin, Halifax

Our research interests focus on the statistical analysis of galaxy redshift and redshift-distance surveys, for the purpose of estimating cosmological parameters and testing cosmological models. In particular, we are interested in developing rigorous statistical techniques for dealing with the impact of observational selection effects, improving the accuracy and calibration of galaxy distance indicators and testing or eliminating the model assumptions on which parameter estimation methods are based. Recent and current research themes include:

Estimating the Hubble Parameter

With Rauzy (formerly Glasgow, now Marseille), Goodwin and Gribbin (Cardiff, Sussex) we have developed a powerful, robust statistical technique for estimating the Hubble parameter from redshift-distance data. This method circumvents completely the problem of Malmquist bias corrections, for long a controversial issue in this field. We have applied the method using HST calibrating galaxies to obtain improved estimates of the Hubble parameter from galaxy linear diameters and Tully-Fisher data (although freed from parametric model assumptions about the linearity of the Tully Fisher relation and the statistical nature of its residuals). We are currently extending the method to other distance indicators.

With Kanbur (Amherst) and Tanvir (UHerts) we are also estimating the Hubble parameter from the HST Cepheid calibration of a range of secondary distance indicators, by developing improved Cepheid distance indicators based their physical properties at maximum light. These improved distance indicators are discussed further below.
 

Testing Models of the Peculiar Velocity Field

With Rauzy we have developed a robust method for comparing velocity field models with galaxy peculiar velocity estimates derived from redshift-distance surveys. The method makes minimal assumptions about the galaxy luminosity function and spatial distribution, and is completely free from Malmquist bias - making it a powerful adjoint to parametric fitting methods such as VELMOD. The method (which we call ROBUST) involves the identification, for each galaxy in a redshift survey, a subset (the grey region in the illustration below) of the data for which luminosity and distance information are separable. We then construct a simple, robust statistic which essentially  expresses the sample correlation between luminosity and distance, given a particular parametric model of the peculiar velocity field. We can then estimate the velocity field parameters by requiring that the sample correlation is zero.

We have applied ROBUST to estimate the linear bias parameter from Mark III and IRAS data. We are currently extending the method to deeper redshift surveys, and to develop diagnostics of large scale bulk motions.

Optimal Representation of the Galaxy Density Field

With Schumacher (formerly Glasgow, now Kiel) and Rauzy we have developed a new orthogonalisation procedure to deal with the effects of an angular mask and radial selection function in reconstructing the galaxy density field from (almost) all-sky redshift surveys. This method addresses the problem that angular and radial selection effects "degrade" the orthonormal properties of spherical harmonic and spherical Bessel  functions, which are commonly used as basis functions in describing the density and peculiar velocity fields. Our approach is an extension to 3-D of earlier work by Gorski which applied a 2-D Gram-Schmidt orthogonalisation procedure to account for the effects of the angular mask in analysing "all-sky" maps of the Cosmic Microwave Background Radiation. Our analysis also incorporates a non-parametric reconstruction of the galaxy selection function, based on the C- method of Lynden-Bell. We have applied these techniques to the recent PSCz survey, and are currently extending the method to deal with redshift space distortions. A projected density map of the PSCz redshift space reconstruction from Schumacher (2001) is shown on the right, and a  redshift-space "slice" of the density field reconstructed in our Local neighbourhood is shown below.

Testing Models of the Galaxy Luminosity Function

With Rauzy we have developed a new robust method for reconstructing the galaxy luminosity function from redshift survey data, combining the statistical efficiency of maximum likelihood techniques with the efficacy of goodness-of-fit tests. An example confidence region plot for the method, applied to test the fit of a Schechter function model to the Southern Sky Redshift Survey Extension, is shown below. We are currently adapting the method to develop diagnostics of luminosity evolution and apply it to photometric redshift data, and with Rauzy and Valls-Gabaud (Toulouse) we are using the method to study the robustness of constraints on the stellar luminosity function derived from HIPPARCOS data.

Improving the Calibration of the Cepheid Distance Scale

With Kanbur and Tanvir we are studying methods to improve the accuracy and calibration of Cepheid variables as extragalactic distance indicators. This work has focussed on the physical properties of Cepheids at maximum light - and in particular the work of Kanbur and collaborators which has indicated that Cepheids show a narrower PL relation, and a narrower range of temperatures, at maximum light. The use of maximum light relations has, of course, clear advantages in observing Cepheids in more distant galaxies, close to the V and I band limit of e.g HST. To this end, we are also developing rigorous statistical tools to reconstruct the shape of Cepheid light curves from noisy and sparsely sampled multicolour data. We are applying fourier decomposition techniques and principal component analysis to define "template" light curves, which are used as prior models in the Bayesian estimation of Cepheid periods, and mean and maximum magnitudes. An example of the reconstructed V and I band light curve of a well-sampled galactic Cepheid is shown on the right.
 

Testing Non-Standard Cosmological Models

With Dabrowski (Sczeczin) we have investigated the compatibility of non-uniform pressure Stephani model universes with recent observations of the Hubble diagram of high-redshift supernovae, exploring the relation between the geometry of the Universe and the "exotic matter" source of the pressure. Barrett (Glasgow) and Clarkson (formerly Glasgow, now Halifax) have extended this analysis to compare supernovae, age and CMBR constraints with Stephani models, and have identified - and resolved - an important loophole in the EGS theorems (which state that an isotropic CMBR implies homogeneity for pressure-free matter) concerning the limits on homogeneity implied by an "almost" isotropic CMBR. With Rauzy we are currently investigating constraints from large scale structure observations on large scale bulk flows and dipole motions in non-standard cosmological models. We are also developing "inverse problem" methods for testing luminosity evolution and inferring the general "Dark Energy" equation of state from observations of high redshift supernovae, such those possible from the proposed SNAP satellite mission.
 

Improving the Tully Fisher Relation

With Salucci and Persic (SISSA) we have developed methods for improving the accuracy and physical basis of spiral galaxy distance indicators, by incorporating rotation curve shape information into the conventional Tully-Fisher relation. Using their "Universal Rotation Curve" model we have explored the impact of shape information on the Tully Fisher relation for the Mathewson spirals sample.